Axes that matter: PCA with a difference

ArXiv ID: 2503.06707 “View on arXiv”

Authors: Unknown

Abstract

We extend the scope of differential machine learning and introduce a new breed of supervised principal component analysis to reduce dimensionality of Derivatives problems. Applications include the specification and calibration of pricing models, the identification of regression features in least-square Monte-Carlo, and the pre-processing of simulated datasets for (differential) machine learning.

Keywords: differential machine learning, principal component analysis, derivatives pricing, least-square Monte-Carlo, dimensionality reduction

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper introduces advanced differential machine learning concepts, including adjoint differentiation and eigenvalue decompositions for supervised PCA, indicating high mathematical density. It includes GitHub links to Python code, specific application examples (e.g., Bermudan options, LS-Monte Carlo), and discusses implementation details for backtesting and calibration, demonstrating strong empirical rigor.

  flowchart TD
    A["Research Goal: Improve dimensionality reduction<br>for Derivatives pricing (DL & ML)"] --> B["Key Methodology: Supervised PCA<br>Differential PCA (dPCA)"]
    B --> C["Data Inputs: Simulated Datasets<br>Features & Sensitivities (Greeks)"]
    C --> D["Computational Process: PCA on<br>‘Axes that Matter’ (Target-Specific)"]
    D --> E["Key Outcomes: Reduced Complexity<br>Better Calibration & Regression"]
    E --> F["Applications: Model Calibration<br>Least-Square Monte-Carlo (LSM)"]